(2x-8)(x+8)=(45)(24)

Solution for (2x-8)(x+8)=(45)(24) equation:

Simplifying
(2x + -8)(x + 8) = (45)(24)

Reorder the terms:
(-8 + 2x)(x + 8) = (45)(24)

Reorder the terms:
(-8 + 2x)(8 + x) = (45)(24)

Multiply (-8 + 2x) * (8 + x)
(-8(8 + x) + 2x * (8 + x)) = (45)(24)
((8 * -8 + x * -8) + 2x * (8 + x)) = (45)(24)
((-64 + -8x) + 2x * (8 + x)) = (45)(24)
(-64 + -8x + (8 * 2x + x * 2x)) = (45)(24)
(-64 + -8x + (16x + 2x2)) = (45)(24)

Combine like terms: -8x + 16x = 8x
(-64 + 8x + 2x2) = (45)(24)

Multiply 45 * 24
-64 + 8x + 2x2 = 1080

Solving
-64 + 8x + 2x2 = 1080

Solving for variable 'x'.

Reorder the terms:
-64 + -1080 + 8x + 2x2 = 1080 + -1080

Combine like terms: -64 + -1080 = -1144
-1144 + 8x + 2x2 = 1080 + -1080

Combine like terms: 1080 + -1080 = 0
-1144 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-572 + 4x + x2) = 0

Factor a trinomial.
2((-26 + -1x)(22 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-26 + -1x)' equal to zero and attempt to solve:

Simplifying
-26 + -1x = 0

Solving
-26 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '26' to each side of the equation.
-26 + 26 + -1x = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -1x = 0 + 26
-1x = 0 + 26

Combine like terms: 0 + 26 = 26
-1x = 26

Divide each side by '-1'.
x = -26

Simplifying
x = -26
Subproblem 2
Set the factor '(22 + -1x)' equal to zero and attempt to solve:

Simplifying
22 + -1x = 0

Solving
22 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-22' to each side of the equation.
22 + -22 + -1x = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -1x = 0 + -22
-1x = 0 + -22

Combine like terms: 0 + -22 = -22
-1x = -22

Divide each side by '-1'.
x = 22

Simplifying
x = 22
Solution
x = {-26, 22}